{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/OJB-Quantum/Maxwell-Boltzmann-Distribution/blob/main/fermion_number_qwell.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "f428b4fc-dbf0-46d7-b7d6-fde375b66323",
      "metadata": {
        "id": "f428b4fc-dbf0-46d7-b7d6-fde375b66323"
      },
      "outputs": [],
      "source": [
        "# EE 5163 Fall 2024\n",
        "# This program calculates the total number of fermions in a 1D quantum well of length L\n",
        "# Install numpy and matplotlib libraries to use it\n",
        "# pip install numpy matplotlib\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Modify the script to result in the entire list of the energy levels and the Fermi Distribution as it changes from 1 to 0 at an energy level of 0.94 eV (where it equals 1 on the Fermi Distr.) and an energy level of 1.13 eV (where it equals 0 on the Fermi Distr.).\n",
        "\n",
        "E_1 should be 0.0094 eV and E_11 should be 1.13 eV, everything else in between can be referenced from the snapshot of the whiteboard.\n",
        "\n",
        "Should push up the Fermi energy to increase the number of electrons in something like"
      ],
      "metadata": {
        "id": "JtyfKHtIzhFX"
      },
      "id": "JtyfKHtIzhFX"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "200ab51c-f58c-498a-9d8e-3c7d6c2b4287",
      "metadata": {
        "id": "200ab51c-f58c-498a-9d8e-3c7d6c2b4287"
      },
      "outputs": [],
      "source": [
        "# Constants\n",
        "# g_some number or gn = degeneracy representing the total possible states (usually up spin and down spin or angular momentum).\n",
        "k_B = 1.380649e-23 # in J/K\n",
        "hbar = 6.626070e-34/(2 * np.pi) # in J.s\n",
        "q0 = 1.602e-19 # fundamental charge in C\n",
        "m = 9.109e-31 # electron rest mass in kg\n",
        "\n",
        "# Parameters\n",
        "m_eff = 0.1*m # effective mass in kg\n",
        "EF = 1 * q0 # Fermi level in Joules\n",
        "L = 20e-9 # Well width in meters. Think of this as the size of your quantum dot.\n",
        "\n",
        "def energy_level(n, L):\n",
        "    \"\"\"Calculate the energy of the nth level in a 1D quantum well of length L.\"\"\"\n",
        "    return (n**2 * np.pi**2 * hbar**2) / (2 * m_eff * L**2)\n",
        "\n",
        "def fermi_dirac(E, EF, T):\n",
        "    \"\"\"Fermi-Dirac distribution function.\"\"\"\n",
        "    return 1.0 / (np.exp((E - EF) / (k_B * T)) + 1)\n",
        "\n",
        "def calculate_total_fermions(L, EF, T, max_n=1000):\n",
        "    \"\"\"Calculate the total number of fermions in the well.\"\"\"\n",
        "    total_fermions = 0\n",
        "    for n in range(1, max_n + 1):\n",
        "        En = energy_level(n, L)\n",
        "        gn = 2\n",
        "        occupation = gn * fermi_dirac(En, EF, T)\n",
        "        total_fermions += occupation\n",
        "\n",
        "        # Stop if the energy level is significantly higher than EF\n",
        "        # if En > EF + 50 * k_B * T:\n",
        "        #     break\n",
        "\n",
        "    return total_fermions\n",
        "\n",
        "    # (# symbol means the number of electrons at each energy level)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "id": "dffa7753-5413-43b6-90db-d2d09d9e1a2a",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dffa7753-5413-43b6-90db-d2d09d9e1a2a",
        "outputId": "fc6ad246-ae29-474d-b6ea-d69877090b12"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "There are 20.0 fermions in the 1d quantum well with EF = 1.0 eV and length L = 20.0 nm\n",
            "There are 19.56187697244321 fermions in the 1d quantum well with EF = 1.0 eV and length L = 20.0 nm \n",
            " \n",
            "\n",
            "First 20 energy levels: \n",
            "\n",
            "E1 = 0.009402186186900287 eV\n",
            "E2 = 0.03760874474760115 eV\n",
            "E3 = 0.08461967568210259 eV\n",
            "E4 = 0.1504349789904046 eV\n",
            "E5 = 0.23505465467250716 eV\n",
            "E6 = 0.33847870272841035 eV\n",
            "E7 = 0.4607071231581141 eV\n",
            "E8 = 0.6017399159616184 eV\n",
            "E9 = 0.7615770811389233 eV\n",
            "E10 = 0.9402186186900287 eV\n",
            "E11 = 1.1376645286149347 eV\n",
            "E12 = 1.3539148109136414 eV\n",
            "E13 = 1.5889694655861484 eV\n",
            "E14 = 1.8428284926324563 eV\n",
            "E15 = 2.1154918920525643 eV\n",
            "E16 = 2.4069596638464734 eV\n",
            "E17 = 2.717231808014183 eV\n",
            "E18 = 3.0463083245556932 eV\n",
            "E19 = 3.394189213471003 eV\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-3-40a8b5b947e8>:19: RuntimeWarning: overflow encountered in exp\n",
            "  return 1.0 / (np.exp((E - EF) / (k_B * T)) + 1)\n"
          ]
        }
      ],
      "source": [
        "# This portion calculates the total number of Fermions in the system at temperature T and Fermi level E_F\n",
        "plt.rcParams['figure.dpi'] = 500\n",
        "\n",
        "T1 = 0.01 # temperature in K\n",
        "T2 = 1000\n",
        "N_fermi1 = calculate_total_fermions(L, EF, T1, max_n=1000)\n",
        "N_fermi2 = calculate_total_fermions(L, EF, T2, max_n=1000)\n",
        "\n",
        "print(f\"There are {N_fermi1} fermions in the 1d quantum well with EF = {EF/q0} eV and length L = {L*1e9} nm\")\n",
        "print(f\"There are {N_fermi2} fermions in the 1d quantum well with EF = {EF/q0} eV and length L = {L*1e9} nm \\n \\n\")\n",
        "\n",
        "Nlvl = 20\n",
        "energies = [en for en in range(1,Nlvl)]\n",
        "\n",
        "print(f\"First {Nlvl} energy levels: \\n\")\n",
        "for i in energies:\n",
        "    e_n = energy_level(i,L)\n",
        "    print(f\"E{i} = {e_n/q0} eV\")\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "fb15f322-3bfe-4329-9656-6b60f7a797b0",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "fb15f322-3bfe-4329-9656-6b60f7a797b0",
        "outputId": "7ce471e1-f9a2-4f95-bd0d-1640555a3033"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-3-40a8b5b947e8>:19: RuntimeWarning: overflow encountered in exp\n",
            "  return 1.0 / (np.exp((E - EF) / (k_B * T)) + 1)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 4000x3000 with 1 Axes>"
            ],
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          },
          "metadata": {}
        }
      ],
      "source": [
        "def plot_fermions_vs_temperature(L, EF1, EF2, T_min, T_max, num_points):\n",
        "    \"\"\"Plot the number of fermions as a function of temperature.\"\"\"\n",
        "    temperatures = np.linspace(T_min, T_max, num_points)\n",
        "    fermion_counts1 = []\n",
        "    fermion_counts2 = []\n",
        "\n",
        "    for T in temperatures:\n",
        "        fermion_count1 = calculate_total_fermions(L, EF1, T)\n",
        "        fermion_count2 = calculate_total_fermions(L, EF2, T)\n",
        "        fermion_counts1.append(fermion_count1)\n",
        "        fermion_counts2.append(fermion_count2)\n",
        "\n",
        "    plt.figure(figsize=(8, 6))\n",
        "    plt.plot(temperatures, fermion_counts1, label=f\"E_F = {EF1/q0} eV\")\n",
        "    plt.plot(temperatures, fermion_counts2, label=f\"E_F = {EF2/q0} eV\")\n",
        "    plt.xlabel(\"Temperature (K)\")\n",
        "    plt.ylabel(\"Number of Fermions\")\n",
        "    # plt.ylim(0,20)\n",
        "    plt.xlim(T_min, T_max)\n",
        "    # plt.title(f\"Number of Fermions vs Temperature (EF = {EF/q0} eV)\")\n",
        "    plt.grid(True)\n",
        "    plt.legend()\n",
        "    plt.show()\n",
        "\n",
        "# Parameters for the temperature range\n",
        "T_min = 1e-3   # Minimum temperature in Kelvin\n",
        "T_max = 2300    # Maximum temperature in Kelvin\n",
        "num_points = 1000  # Number of temperature points\n",
        "\n",
        "# Plot the number of fermions as a function of temperature\n",
        "EF1 = 4 * q0;\n",
        "EF2 = 4 * q0;\n",
        "\n",
        "plot_fermions_vs_temperature(L, EF1, EF2, T_min, T_max, num_points)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e2b39a67-3923-43de-99f9-c559ea0618bd",
      "metadata": {
        "id": "e2b39a67-3923-43de-99f9-c559ea0618bd"
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.12.5"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}